. For x ER, defineF(x) =(-1) ²nn!n=0(a) Prove that the series converges for any x and that the convergence is uniform onany closed interval.(b) We will show in class that F(x) = e-². Using this fact, find (with proof) a seriesthat converges toG(x) = f* efe-²dt.

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Answered: For x ER, define F(x)= (-1)"x²n n! n=0…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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For x ER, define F(x)= (-1)"x²n n! n=0 (a) Prove that the series converges for any x and that the convergence is uniform on any closed interval. (b) We will show in class that F(x) = e-¹². Using this fact, find (with proof) a series that converges to PI G(x) = | e- dt.